Various devices for tightening straps notched on one of their faces are known in the art. These usually comprise a pivoting tensioning element itself having, on a portion of its periphery, a tooth cooperating with the teeth of the strap. Such a device is disclosed, e.g., in French Pat. No. 2,180,250. This known device assures increasing tensioning of the strap by pivoting of the movable element in one direction, and it comprises auxiliary means for retention of the strap when the latter has reached a tension corresponding to the desired degree of tightening. Such prior art devices, however, usually have rather complex structures and require inconvenient operations for eliminating the tightening tension on the strap when the latter is to be freed.